There are three ways that each box can be oriented. That is, there are three ways that you can traverse four sides of the box and return to the start. The following picture illustrates the three options.
For each box, only one of the three options allows you to traverse four sides with each side being a different color. Once you find the orientation for each box that has all four colors in the correct sequence, it is a simple matter to position the boxes in a row to satisfy the puzzle requirement.